Derivation of Control Parameters of Fuel Cell Systems for Flexible Fuel Operation

ABSTRACT

A method of operating a fuel cell system includes characterizing the fuel or fuels being provided into the fuel cell system, characterizing the oxidizing gas or gases being provided into the fuel cell system, and calculating at least one of the steam:carbon ratio, fuel utilization and oxidizing gas utilization based on the step of characterization.

The present application is a continuation of U.S. application Ser. No.12/149,816 filed on May 8, 2008, and incorporated herein by reference inits entirety.

BACKGROUND OF THE INVENTION

The present invention relates generally to the field of fuel cellsystems and more particularly to parameterized control of fuel cellsystems to allow for efficient operation under various atmosphericconditions and with various fuel sources.

Fuel cells are electrochemical devices which can convert energy storedin fuels to electrical energy with high efficiencies. High temperaturefuel cells include solid oxide and molten carbonate fuel cells. Thesefuel cells may operate using hydrogen and/or hydrocarbon fuels. Thereare classes of fuel cells, such as the solid oxide reversible fuelcells, that also allow reversed operation, such that water or otheroxidized fuel can be reduced to unoxidized fuel using electrical energyas an input.

In a high temperature fuel cell system such as a solid oxide fuel cell(SOFC) system, an oxidizing gas is passed through the cathode side ofthe fuel cell while a fuel flow is passed through the anode side of thefuel cell. The oxidizing gas is typically air, while the fuel flow istypically a hydrogen-rich gas created by reforming a hydrocarbon fuelsource. Water may also be introduced into the system in the form ofsteam. The fuel cell, typically operating at a temperature between 750°C. and 950° C., enables the transport of negatively charged oxygen ionsfrom the cathode flow stream to the anode flow stream, where the ionscombine with either free hydrogen or hydrogen in a hydrocarbon moleculeto form water vapor and/or with carbon monoxide to form carbon dioxide.The excess electrons from the negatively charged ions are routed back tothe cathode side of the fuel cell through an electrical circuitcompleted between anode and cathode, resulting in an electrical currentflow through the circuit.

SUMMARY OF THE INVENTION

The first embodiment of the invention is a method of operating a fuelcell system in which the fuel and/or oxidizing gas being provided intothe fuel cell system are characterized and at least one of thesteam:carbon ratio, fuel utilization and oxidizing gas utilization iscalculated based on this characterization.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In fuel cells utilizing air as the oxidizing gas, fuel cell operation istypically controlled such that the steam:carbon ratio, fuel utilization,and oxidizing gas utilization stay within nominal operation ranges.However, various fuel sources with differing carbon contents can be usedin fuel cell operation. This, along with variations in local atmosphericconditions, can cause the actual steam:carbon ratio, fuel utilization,and oxidizing gas utilization to deviate from values of these parametersderived from calculations based on assumptions of fuel and aircomposition.

Given the potential deployment of fuel cell systems in a multitude oflocations, each subject to variances in fuel composition and localatmospheric conditions, it is desirable to have a relatively fewsimplified parameters to characterize the fuel and oxidizing gas forcontrol of fuel cell systems. Such simplified parameterized control hasthe added benefit of easing the transition from one fuel source toanother while the fuel cell is under load or enabling the utilization ofa plurality of fuels, oxidation gases, or both, at the same time.

The inventors realized that parameterized control of fuel cell systemoperation can be accomplished through the use of a few derivedquantities (i.e., steam:carbon (S:C) ratio, fuel utilization, andoxidizing gas utilization) and that simplified derivation of thesequantities can be accomplished through calculations based oncharacterizing fuel composition and oxidizing gas composition. Ininstances where the oxidizing gas is air, local atmospheric conditionscan be used to derive the oxidizing gas composition.

Additionally, the inventors realized that parameterized control of fuelcell systems with these few derived quantities can aid in the operationof a fuel cell system utilizing a plurality of fuels and/or a pluralityof oxidizing gases. This is especially useful to facilitate transitionfrom one fuel to another while under load or operation of the fuel cellwith a plurality of fuel sources.

Preferably the fuel cell system to be controlled contains one or moresolid oxide fuel cell (SOFC) stacks. A detailed description of a type ofSOFC system is described in U.S. patent applications Ser. No. 11/491,487(filed on Jul. 24, 2006) and Ser. No. 11/002,681 (filed on Dec. 3,2004), both hereby incorporated by reference in their entirety.

A practical fuel cell system, such as a SOFC system, can compriseelements which include but are not limited to: steam generator(s),reformer(s), heat exchanger(s), blower(s), condenser(s), vent(s),mixer(s), catalytic reactor(s) or any combination thereof.

“Catalytic reactor” as used herein describes an element in a fuel cellsystem capable of catalyzing a reaction between reactants conveyedthereto. These reactors typically comprise metal catalyst-containingtubes or other conduits. Catalytic reactors may be located at variousplaces in a fuel cell system. Examples of catalytic reactors include,but are not limited to catalytic partial oxidation (CPOx) reactors andanode tail gas oxidation (ATO) reactors. A detailed description of atype of catalytic reactor is described in U.S. patent application Ser.No. 11/703,153 (filed on Feb. 7, 2007), which is hereby incorporated byreference in its entirety.

A CPOx reactor, for example, may be used in the start-up mode of a fuelcell system utilizing air as the oxidizing gas, to make the systemindependent of an external source of hydrogen. In this example, the CPOxunit produces hydrogen, water vapor, CO and CO₂ from the air and fuelmixture.

As used herein, the term “CPOx flow rate” is used to express thequantity of oxidizing gas introduced into a CPOx reactor. The oxidizinggas introduced into a COPx reactor is typically but not limited to air.The measurement of flow rate can be expressed in units of standardliters per minute (SLPM), although one skilled in the art wouldrecognize that these units can readily be converted into moles persecond.

As used herein, the term “water flow rate” is used to express the sum ofthe quantity of water introduced into the fuel cell stack or system withthe fuel and the anode recycle water, if present. Water introduced intothe fuel cell stack or system typically will be in the form of vapor,i.e., steam. Typically this measurement is expressed in units ofstandard liters per minute (SLPM), although one skilled in the art wouldrecognize that these units can readily be converted into moles persecond.

As used herein, the term “fuel flow rate” is used to express thequantity of fuel introduced into the fuel cell. Typical fuels for fuelcell operation are fuels comprising hydrogen and carbon. Examples oftypical fuels for fuel cell operation include but are not limited tohydrocarbons (including methane, ethane and propane), natural gas,alcohols (including ethanol), and syngas derived from coal or naturalgas reformation. Typically this measurement is expressed in units ofstandard liters per minute (SLPM), although one skilled in the art wouldrecognize that these units can readily be converted into moles persecond.

As used herein, the term “fuel composition” refers to the elementalcomposition of fuel. This elemental composition is typically expressedin moles [X] per mole of fuel, where [X] is an element of interest.Examples of elements of interest useful for the determination of theparameters contained herein include carbon, oxygen, hydrogen andoptionally nitrogen. For liquid based fuels, elemental composition mayalso be expressed as moles [X] per milliliter of fuel or moles [X] pergram of fuel.

As used herein, the term “cathode flow rate” is used to express thequantity of oxidizing gas introduced at the cathode of the fuel cell.The oxidizing gas introduced into at the cathode is typically but notlimited to air. The measurement of flow rate can be expressed in unitsof standard liters per minute (SLPM), although one skilled in the artwould recognize that these units can readily be converted into mol/sec.

As used herein, the term “ambient pressure” indicates absoluteatmospheric pressure. Typically, this measurement is expressed in unitssuch as pounds per square inch absolute (PSIA) or kilopascals (kPa).

As used herein, the term “alcohol” is used to generally indicate anorganic compound derivitized with a hydroxyl group. Examples of alcoholsinclude, but are not limited to methanol, ethanol and isopropyl alcohol.

Steam:Carbon Ratio

In one embodiment of the invention, the control parameter steam:carbon(S:C) ratio is derived from water flow rate, fuel flow rate, and carboncomposition of the fuel (expressed as moles of carbon per moles offuel). The water flow rate and fuel flow rate are variable quantitiesthat can be adjusted by the operator to keep the S:C ratio within anominal operating range. The fuel composition may be theoreticallyderived from the composition of the fuel used.

For example, if methane gas (i.e., CH₄) is used for fuel, thenstoichiometric analysis indicates that there is one mole of carbon forevery one mole of fuel. However, if ethanol (i.e., CH₃CH₂OH) is used,stoichiometric analysis indicates that there are two moles of carbon forevery one mole of fuel. As it is possible that sources of fuel for fuelcell systems may be mixtures of unknown quantities of two or more fuels,such theoretical stoichiometric analysis may not always be suitable. Insuch cases, characterization of the carbon content of the fuel may beobtained from other sources, i.e., through direct detection or gatheringthe information from the commercial provider of the fuel.

Once the carbon content of the fuel is determined or obtained, the S:Cratio can be derived as follows. The S:C ratio is equal to the waterflow rate divided by the fuel flow rate multiplied by carbon content ofthe fuel:

S:C ratio=Water Flow Rate/Carbon Flow Rate;

where Carbon Flow Rate=Fuel Flow Rate*mol C/mol Fuel;

and Water Flow Rate=Molar Flow Rate of Steam from the steamgenerator+Anode Recycle Flow Rate*Mole Fraction of Water in the AnodeRecycle Stream.

In alternative methods, carbon content of the anode recycle stream (inthe form of CO and CO₂) is also included in the Carbon Flow Rate.Similarly, in alternative methods, CO₂ content of the fuel stream isincluded in the Carbon Flow Rate. Inclusion of the contribution from CO₂to the Carbon Flow Rate is more important in systems where the fuel isbiogas, which typically will have a much greater fraction of CO₂ thanother fuel sources.

The amount of fuel and steam being introduced into a fuel cell can bevaried continuously or intermittently to preferably maintain the S:Cratio in the fuel inlet stream during operation of the fuel cell stackwithin a nominal operating range; said nominal operating range between,2:1 to 2.5:1 S:C; preferably between 2:1 and 2.3:1 S:C.

Fuel Utilization and Air Utilization

The control parameter fuel utilization is derived from the average cellcurrent, total number of cells and fuel available. Fuel available is aderived quantity based on fuel composition information, fuel flow rate,CPOx flow rate, and oxygen content of the oxidizing gas at the CPOx.

The control parameter oxidizing gas utilization is derived from theaverage cell current, total number of cells, cathode flow rate, and theoxygen content of the oxidizing gas at the cathode.

To derive either of these control parameters, it is first necessary tocharacterize the oxidizing gas(es) introduced into the fuel cell system(i.e., to determine % O₂ in oxidizing gas(es) introduced at the CPOx andthe cathode). In instances where an oxidizing gas introduced at the CPOxand/or cathode is a gas other than air, the percent oxygen can bedetected, or more typically, obtained from the commercial source of thatoxidizing gas. In instances where air is used as an oxidizing gas at oneor both of the CPOx and/or cathode, % O₂ can be determined withcalculations utilizing local atmospheric information including ambienttemperature, ambient pressure, and relative humidity.

Characterization of Air to Determine % O₂

First, it must be understood that air is a mixture comprising variousgaseous components, predominantly comprising N₂, O₂ and H₂O. The CRCHandbook of Chemistry and Physics states that the composition of dry airis: 78.084% N₂, 20.946% O₂, and 0.97% comprising many other tracecomponents. For calculation purposes, the trace component can be lumpedin with N₂, so that the dry composition of air can be considered to be20.946% O₂ and 79.054% N₂. Further, treating air as an ideal gas, thetotal atmospheric pressure of the mixture is the summation of thepartial pressures of the individual components of the mixture.

The water vapor content of air is not constant. As the water vaporcontent of air increases, the nitrogen and oxygen content decrease,while maintaining the N₂:O₂ ratio of dry air. Thus, in order to derive %O₂ in air, water vapor's contribution to atmospheric pressure must besubtracted. The contribution of water vapor to the atmospheric pressureis highly variable and can range from approximately 0%-5%. This is, inpart, because the equilibrium vapor pressure of water vapor variessignificantly with temperature.

Common atmospheric data, such as the ambient temperature and relativehumidity, can be used to determine water vapor's contribution to theambient atmospheric pressure. Relative humidity (RH) is a measure of thepercentage of the equilibrium vapor pressure of water that is actuallyfound in a given sample of air. Thus, the partial pressure of watervapor in air (P_(H2O)) (i.e., water vapor's contribution to ambientatmospheric pressure) is easily determined by referring to datadescribing water's equilibrium vapor pressure at various temperatures(P*_(H2O)) and multiplying the value for water's equilibrium vaporpressure at the ambient temperature by the relative humidity:

P _(H2O) =P* _(H2O)*RH.

Data describing water equilibrium vapor pressure at various temperaturesis well known in the art and can be found, for example, in tabularformat in the CRC Handbook of Chemistry and Physics. Alternatively, thevapor pressure of water has typically been traditionally correlated as afunction of temperature with the Antoine Equation (Reid Prausnitz andPoling, The Properties of Gases and Liquidshttp://www.amazon.com/exec/obidos/ASIN/0070517991/hyperadcommuni02), ormore rigorously with equations published by the National Bureau ofStandards http://orion.math.iastate.edu/burkardt/f_src/steam/steam.html

P_(H2O) can then be subtracted from the ambient atmospheric pressure(P_(ambient)), with the remaining pressure resulting from thecontribution of the partial pressures of O₂ and N₂ (P_(O2) and P_(N2)):

P _(ambient) −P _(H2O) =P _(O2) +P _(N2).

Now, utilizing the ratio 20.94 O₂:79.06 N₂, P_(O2) and P_(N2) can bedetermined:

P _(O2)=0.2094*(P _(ambient) −P _(H2O));

P _(N2)=0.7906*(P _(ambient) −P _(H2O)).

Finally, the % O₂ and % N₂ are calculated as the percent P_(O2) andP_(N2) are of P_(ambient):

% O₂(mol %)=(P _(O2) /P _(ambient))*100%;

% N₂(mol %)=(P _(N2) /P _(ambient))*100%.

The common local atmospheric data used in this determination (i.e.,ambient temperature, ambient pressure and relative humidity) can bemonitored on-site or readily obtained from a local weather data source.

Fuel Available (in mol e⁻/sec)

Derivation of the control parameter fuel utilization also requires thedetermination of the fuel available. Calculation of the fuel availablecan be based on the number oxygen anions required to fully oxidize thefuel, or the DC electrical equivalent in moles of electrons. Theanalysis below is presented on the basis of the DC electrical equivalentof the oxygen anions required to fully oxidize the fuel. The fuelavailable is based on the fuel flow rate(s), and the C, H, O andoptionally N composition of the fuel. It is then corrected for anyportion of the fuel that is already oxidized in the CPOx reactor. Ifnitrogen in the fuel is not oxidized (i.e. it leaves the fuel cell asN₂), then nitrogen is not considered when determining the fuelavailable.

Fuel Available (in mol e ⁻/sec)=(4*C atom/mole Fuel+H atoms/moleFuel−2*O Atoms/mole Fuel)*Fuel Flow (in mol/sec)−4*(mol O₂/mol CPOxflow)*CPOx flow (in mol/sec);

Fuel Utilization (%)

Once the quantity of fuel available is known, the control parameter fuelutilization is derived according to the following equation:

Fuel Utilization (%)=100%*((Average Cell Current (in Amps)*Number ofCells)/F)/Fuel Available (in mol e ⁻/sec);

where F=Faraday's constant.Oxidizing Gas Available (in mol e⁻/sec)

Similar to the derivation of fuel utilization, derivation of oxidizinggas utilization also requires determination of the oxidizing gasavailable. Calculation of oxidizing gas available below is based on airas the oxidizing gas, cathode flow, and mole fraction of O₂ in theoxidizing gas (i.e., % O₂):

Oxidizing Gas Available (in mol e ⁻/sec)=4*(% O₂/100%)*Cathode Flow (inmol/sec);

Oxidizing Gas Utilization (%)

Once the quantity of oxidizing gas available is know, the controlparameter oxidizing gas utilization is derived according to thefollowing equation:

Oxidizing Gas Utilization (%)=100%*((Average Cell Current (inAmps)*Number of Cells)/F)/Oxidizing Gas Available (in mol e ⁻/sec);

where F=Faraday's constant.Transition from One Fuel to Another/Utilization of a Plurality of Fuels

In a second embodiment of the invention, calculations described aboveused to derive certain control parameters are modified in order tofacilitate the gradual transition from one fuel to another while thefuel cell is under load or to account for differences in the compositionof each fuel during the continued operation of a fuel cell utilizing aplurality of fuels with distinct carbon contents, hydrogen contents,and/or oxygen contents.

Accounting for use of a plurality of fuels with differing compositions,either as a transient condition when switching from one fuel to anotheror as a continuing condition when operating the fuel cell with multiplefuels, requires adjusting the calculations described above for thequantities of the S:C ratio and fuel available.

S:C Ratio (Multiple Fuels)

The S:C ratio for multiple fuels (i.e., fuel₁, fuel₂, . . . , fuel_(x))is calculated according to the following equation:

S:C Ratio (Multiple Fuels)=Water Flow Rate/(Carbon FlowRate)_(cumulative);

where (Carbon Flow Rate)_(cumulative)=Σ(Fuel_(n) Flow Rate*(mol Catoms/mol Fuel_(n))); and

n=1 to x.

Fuel Available (Multiple Fuels)

Similarly, the fuel available from multiple fuels (i.e., fuel₁, fuel₂, .. . , fuel_(x)) is calculated according to the following equation:

Fuel Available (Multiple Fuels) (in mol e ⁻/sec)=(mol e ⁻/sec fromFuel)_(cumulative)−((mol e ⁻/mol CPOx flow)*CPOx flow (in mol/sec));

where (mol e ⁻/sec from Fuel)_(cumulative)=Σ(4*(mol C atoms/molFuel_(n))+(mol H atoms/mol Fuel_(n))−2*(mol O atoms/mol Fuel_(n)))

n=1 to x; and

mol e ⁻/mol CPOx Flow=4*(% O₂)/100%.

Having completed the derivation of the fuel available from multiplefuels, the overall fuel utilization is calculated according to theequation described above.

Transition from One Oxidizing Gas to Another/Utilization of a Pluralityof Oxidizing Gases

While it is unlikely to be necessary, the calculations described aboveused to derive certain control parameters can be modified in order tofacilitate the gradual transition from one oxidizing gas to anotherwhile the fuel cell system is under load or to account for differencesin the oxygen content of each oxidizing gas during the continuedoperation of a fuel cell utilizing a plurality of oxidizing gases.

If necessary, utilization of a plurality of oxidizing gases is mostlikely to occur under conditions where an air stream partially depletedin oxygen (such that the O₂ content was ˜15-21%) was available atpressures of 1-5 psig as a primary source of oxidizing gas. Under suchconditions, it may be desirable to supplement the primary oxidizing gasflow with a second oxidizing gas having a higher O₂ concentration.

Accounting for use of a plurality of oxidizing gases with differingoxygen contents, either as a transient condition when switching from oneoxidizing gas to another or as a continuing condition when operating thefuel cell with multiple oxidizing gases, requires adjusting thecalculations described above for the quantities of fuel available andoxidizing gas available.

Fuel Available (Multiple Oxidizing Gases)

If the oxidizing flow at the CPOx is a mixture of two or more oxidizinggases (i.e., oxidizing gas₁ oxidizing gas₂, . . . , oxidizing gas_(y)),the fuel available is calculated according to the following equation:

Fuel Available (Multiple Oxidizing Gases) (in mol e ⁻/sec)=(4*Catom/mole Fuel +H atoms/mole Fuel−2*O atoms/mole Fuel)*Fuel Flow (inmol/sec)−Σ((mol e ⁻/mol CPOx Flow_(m))*CPOx Flow_(m)(in mol/sec));

where mol e ⁻/mol CPOx Flow_(m)=4*(% O₂)_(m)/100%;

-   (% O₂)_(m) is the oxygen content of oxidizing gas_(m);-   CPOx Flow_(m) is the flow rate of oxidizing gas_(m) at the CPOx; and-   m=1 to y.

Having completed the derivation of the fuel available with multipleoxidizing gases, the overall fuel utilization is derived as describedabove.

Oxidizing Gas Available (Multiple Oxidizing Gases)

Similarly, derivation of oxidizing gas available from a mixture of twoor more oxidation gases (i.e., oxidizing gas₁, oxidizing gas₂, . . . ,oxidizing gas_(y)), is calculated according to the following equation:

Oxidizing Gas Available (Multiple Oxidizing Gases) (in mol e⁻/sec)=Σ((mol e ⁻/mol Oxidizing Gas_(m))*(Cathode Oxidizing Gas_(m)Flow) (in mol/sec));

where mol e ⁻/mol Oxidizing Gas_(m)=4*(% O₂)_(m)/100%;

-   Cathode Oxidizing Gas_(m) Flow is the flow rate of oxidizing gas_(m)    at the cathode; and-   m=1 to y.

Having completed the derivation of the oxidizing gas available frommultiple oxidizing gases, the overall oxidizing gas utilization isderived as described above.

Multiple Fuels and Oxidizing Gases

In additional related embodiments, the modifications of the calculationsto account for multiple fuels (e.g. fuel₁, fuel₂, . . . , fuel_(x)) andmultiple oxidizing gases (oxidizing gas₁, oxidizing gas₂, . . . ,oxidizing gas_(y)) can be combined to allow for derivation of controlparameters of a fuel cell system operating with a plurality of fuels anda plurality of oxidizing gases. No modifications beyond those describedabove are required for the S:C ratio and oxidizing gas available.However, the derivation of fuel available requires the additionalmodification:

Fuel Available (Multiple Fuel and Oxidizing Gases) (in mol e ⁻/sec)=(mole ⁻/sec from Fuel)_(cumulative)−Σ((mol e ⁻/mol CPOx Flow_(m))*CPOxFlow_(m) (in mol/sec));

where (mol e ⁻/sec from Fuel)_(cumulative)=Σ(4*(mol C atoms/molFuel_(n))+(mol H atoms/mol Fuel_(n))+2*(mol O atoms/mol Fuel_(n));

mol e ⁻/mol CPOx Flow_(m)=4*(% O₂)_(m)/100%;

-   (% O₂)_(m) is the oxygen content of oxidizing gas_(m);-   CPOx Flow_(m) is the flow rate of oxidizing gas_(m) at the CPOx;-   n=1 to x; and-   m=1 to y.

Having completed the derivation of the fuel available with multiplefuels and oxidizing gases, the overall fuel utilization is derived asdescribed above.

Preferred Fuel Utilization and Oxidizing Gas Utilization Ranges

Certain fuel cell systems which produce hydrogen and electricity, suchas in systems described in U.S. applications Ser. No. 10/446,704 (filedon May 29, 2003) and Ser. No. 11/491,487 (filed on Jul. 24, 2006), bothincorporated by reference in their entirety, can operate in a number ofmodes, for example to optimize electrical efficiency, optimize hydrogenproduction, or to balance the two. While in these systems the preferredoxidizing gas utilization range remains the same regardless of theoperating mode, preferred fuel utilization ranges vary depending on thedesired operating mode.

The preferred oxidizing gas utilization range is 10-60%, more preferably25-40%.

When the system is operated to optimize electricity generation (i.e., tooptimize the AC electrical efficiency of the system), fuel utilizationis maximized to the highest reasonable operating value, such as about75% to 90%, for example.

When the system is operated to optimize hydrogen generation, fuelutilization is minimized to the lowest reasonable operating value, suchas about 55% to 60%, for example. Furthermore, more hydrocarbon fuel maybe provided to the fuel cell stack when the system operates to optimizehydrogen production than when the system operates to optimize electricalefficiency. For example, 50% to 100% more hydrocarbon fuel may beprovided when the system is operating to optimize hydrogen productionthan when the system is operating to optimize electrical efficiency.

Computer Assisted Control of Fuel Cell Systems through AutomatedCalculation of Control Parameters

In another embodiment of the invention, a generic or specializedcomputer or another suitable logic device, such as microprocessor orASIC, is used to perform the calculations of the above described controlparameters. In certain related embodiments, data generated by sensorscapable of measuring local atmospheric conditions useful for the abovedescribed calculations may be accessible by the computer. In otherrelated embodiments, data generated by sensors capable of directcharacterization of the elemental composition of fuel to be entered intothe fuel cell system may be accessible by the computer. Data fromsensors may be transmitted to the computer either wirelessly or throughwires. In other related embodiments, local atmospheric and/or fuelcomposition information may be manually entered into the computer foruse in the calculations. In still other related embodiments, thecomputer may obtain local atmospheric and/or fuel compositioninformation from a local weather data source and/or a fuel suppliereither wirelessly, through wires, or via the internet.

In additional related embodiments, the computer may be attached to adisplay apparatus, such as a display monitor, to display the results ofthe calculated control parameter(s). In these embodiments, the operatorof a fuel cell system can utilize the displayed output to determinenecessary adjustments to fuel, oxidizing gas and/or water flows into thesystem so that the control parameter(s) reach and/or stay withinpreferred operational ranges.

In other related embodiments, the computer used to perform thecalculations or another computer networked with the computer performingthe calculations may also be used to control the flow of fuel, oxidizinggas and/or water into the fuel cell system. In these embodiments, thecomputer can utilize the results of the calculations to determine thenecessary adjustments to fuel, oxidizing gas and/or water flows into thesystem so that the control parameter(s) reach and/or stay withinpreferred operational ranges.

EXAMPLES Example 1 Characterization of Air Under Two DifferentAtmospheric Conditions

As a demonstration of the characterization of air, the determination ofthe water, oxygen and nitrogen contents of air under two different setsof atmospheric conditions were conducted. The results of thesedeterminations are found in Table 1.

Water, oxygen and nitrogen content of air at an ambient temperature of22° C., ambient pressure of 14.696 psia, and relative humidity of 70%were derived by following the methods described above. The equilibriumvapor pressure of water at 22° C. was obtained from parameters publishedin the DIPPR 801 project.

Water, oxygen and nitrogen content of air at an ambient temperature of30° C., ambient pressure of 14 psia, and relative humidity of 70% werealso derived by following the methods described above. The equilibriumvapor pressure of water at 30° C. was obtained from DIPPR parameters.

TABLE 1 Water, Oxygen and Nitrogen Content of Air at Two Exemplary Setsof Atmospheric Conditions Ambient Pressure (psia) 14.696 14 AmbientTemperature (° C.) 22 30 Ambient Relative Humidity (%) 70 70 H₂O Contentof Air (mol %) 1.83 3.08 O₂ Content of Air (mol %) 20.56 20.30 N₂Content of Air (mol %) 77.61 76.62

Example 2 Determination of S:C Ratio

Various exemplary fuel sources were characterized for demonstration ofderivation of control parameters, including S:C ratios. Table 2 containsthe elemental composition and lower heat value (LHV) of three possiblefuel sources: methane, natural gas and propane. Fuels may be identifiedby LHV, and overall efficiency may be calculated as Total powerout/Total heat content in. The data listed for natural gas is merelyexemplary; the elemental composition of natural gas may vary over timeand by source. Thus, the characterization of natural gas will have to bedetected or obtained at the time of use.

TABLE 2 Characterization of Exemplary Fuels Parameter Methane NaturalGas Ethanol Propane mol C atoms/mol Fuel 1 1.02 2 3 mol H atoms/mol Fuel4 3.99 6 8 mol O atoms/mol Fuel 0 0.016 1 0 mol N atoms/mol Fuel 0 0.0180 0 LHV of the Fuel 0.5968 0.6003 0.9183 (in kw/SLPM)

These values can be used to determine the S:C ratios as described abovefor the following exemplary flow rates: 90 SLPM water and 30 SLPMmethane; 90 SLPM water and 30 SLPM natural gas; 90 SLPM water and 15SLPM ethanol; and 90 SLPM water and 10 SLPM propane. Use of methane,natural gas, ethanol and propane under the above listed operatingconditions yields S:C ratios of 3.0, 2.94, 3.0 and 3.0 respectively:

S:C ratio_(methane)=90 SLPM H₂O/(30 SLPM Methane*1 mol C atoms/1 molfuel)=3.0;

S:C ratio_(natural gas)=90 SLPM H₂O/(30 SLPM Natural Gas*1.02 mol Catoms/1 mol fuel)=2.94;

S:C ratio_(ethanol)=90 SLPM H₂O/(15 SLPM Ethanol*2 mol C atoms/1 molfuel)=3.0; and

S:C ratio_(propane)=90 SLPM H₂O/(10 SLPM Propane*3 mol C atoms/1 molfuel)=3.0.

As seen above, differing flow rates may be required for various types offuels to operate a fuel cell system at similar S:C ratios. Additionally,each of the S:C ratios derived above are at or near a value of 3, thusindicating to an operator of a fuel cell system, or computer operating afuel cell system, that one or both of the fuel and water flow rates needto be adjusted to compensate for the characteristics of the particularfuel utilized. In each of the exemplary cases shown above, the S:C ratiocan be lowered to an optimal value through appropriately lowering waterflow, increasing fuel flow, or a combination of the two.

Example 3 Derivation of Fuel Utilization with a Single Fuel and Air asOxidizing Gas

The control parameter fuel utilization was derived for a fuel cellsystem containing 400 cells to generate 10 Amps of current while usingNatural Gas as fuel at a flow rate of 10 SLPM, air as an oxidizing gasat 300 SLPM and no air at the CPOx. Ambient atmospheric conditions wereambient temperature of 30 C, ambient pressure of 14 psia, and relativehumidity of 70%. Under these atmospheric conditions, air has 20.30% O₂(see Example 1 above).

Using the relevant data in the equation for fuel available describedabove, the fuel available is calculated to be 0.05978 mole e-/sec:

Fuel Available (in mol e ⁻/sec)=4*(1.0202 mol C atoms/mol NaturalGas)+(3.9904 mol H atoms/mol Natural Gas)−2*(0.0160 mol O atoms/molNatural Gas*10 SLPM Natural Gas*(1 min/60 sec)*(1 mol/22.4136 standardliters)−4*(20.30% O₂)/100%.*0.0 SLPM CPOx flow=0.05978 mole e-/sec

With this know quantity of fuel available, the control parameter fuelutilization is derived as follows:

Fuel  Utilization  (%) = 100% * ((10  Amps) * 400  Cells)/                        F)/(0.05978  mole  e-/sec ) = 69.35%

where F=Faraday's constant.

Thus under these flow and atmospheric conditions, the fuel utilizationis 69.35%. This value would indicate to an operator of a fuel cellsystem, or a computer operating a fuel cell system, that the fuelutilization is lower than desired, and the fuel flow rate could bedecreased, thereby increasing fuel utilization and decreasing costs.

Example 4 Derivation of Oxidizing Gas Utilization with a Single Fuel andAir as Oxidizing Gas

The operating conditions from above (i.e., system specifications, flowrates and ambient atmospheric conditions found in Example 3) were usedto determine the control parameter oxidizing gas utilization. Underthese atmospheric conditions, air has 20.30% O₂ (see Example 1 above).

Using the relevant data in the equation for oxidizing gas availabledescribed above, the oxidizing gas available is calculated to be 22.89%:

Oxidizing Gas Available (in mol e ⁻/sec)=4*(20.30% O₂)/100%*300 SLPMmain air*(1 min/60 sec)*(1 mol/22.4136 standard liters)=0.1811 mole-/sec

Once the quantity of oxidizing gas available is know, the controlparameter oxidizing gas utilization is derived as follows:

Oxidizing Gas Utilization (%)=100%*((10 Amps)*400 Cells)/F)/(0.1811 mole ⁻/sec)=22.89%

where F=Faraday's constant.

Thus under these oxidizing flow and atmospheric conditions, theoxidizing gas utilization is 22.89%. This value would indicate to anoperator of a fuel cell system, or a computer operating a fuel cellsystem, that air utilization is lower than desired, and main air flowcould be decreased.

The foregoing description of the invention has been presented forpurposes of illustration and description. The methods and devicesillustratively described herein may suitably be practiced in the absenceof any element or elements, limitation or limitations, not specificallydisclosed herein. Thus, for example, the terms “comprising”,“including,” containing”, etc. shall be read expansively and withoutlimitation. Additionally, the terms and expressions employed herein havebeen used as terms of description and not of limitation, and there is nointention in the use of such terms and expressions of excluding anyequivalents of the features shown and described or portions thereof, butit is recognized that various modifications are possible within thescope of the invention claimed. Thus, it should be understood thatalthough the present invention has been specifically disclosed bypreferred embodiments and optional features, modification and variationof the invention embodied therein herein disclosed may be resorted to bythose skilled in the art, and that such modifications and variations areconsidered to be within the scope of this invention. It is intended thatthe scope of the invention be defined by the claims appended hereto, andtheir equivalents.

1. A method of operating a fuel cell system, comprising: characterizingat least one of a fuel and an oxidizing gas being provided into the fuelcell system; calculating at least one of fuel utilization and oxidizinggas utilization based on the steps of characterizing the at least one ofthe fuel and the oxidizing gas.
 2. The method of claim 1, furthercomprising: determining a flow rate of water introduced into the fuelcell system; and calculating a steam:carbon (S:C) ratio.
 3. The methodof claim 2, wherein: the fuel being provided into the fuel cell systemcomprises a mixture of two or more fuels; the step of characterizing thefuel comprises characterizing the mixture of the two or more fuels; andcalculating the S:C ratio comprises calculating the S:C ratio based onthe step of characterizing the mixture of the two or more fuels.
 4. Themethod of claim 3, wherein the two or more fuels comprise two or morefuels with distinct carbon contents, hydrogen contents, and/or oxygencontents.
 5. The method of claim 4, wherein: the step of characterizingat least one of a fuel and an oxidizing gas comprising characterizingboth the fuel and the oxidizing gas; the oxidizing gas comprises air;local atmospheric information is used to characterize the air; and thelocal atmospheric information comprises ambient temperature, ambientpressure and relative humidity.
 6. The method of claim 2, furthercomprising: providing the fuel and the oxidizing gas to the fuel cellsystem based on the calculated S:C ratio, fuel utilization or oxidizinggas utilization; and generating electricity using the fuel cell system.7. The method of claim 2, wherein the S:C ratio is calculated accordingto following formula: S:C ratio=Water Flow Rate/(Fuel Flow Rate*molC/mol Fuel).
 8. The method of claim 1, wherein the step ofcharacterizing at least one of a fuel and an oxidizing gas comprisescharacterizing the oxidizing gas.
 9. The method of claim 8, wherein: theoxidizing gas being provided into the fuel cell system is air; localatmospheric information is used for the characterizing the oxidizinggas; and the local atmospheric information comprises ambienttemperature, ambient pressure and relative humidity of the air.
 10. Themethod of claim 8, wherein the oxidizing gas is air and the step ofcharacterizing the oxidizing gas utilizes ambient pressure, temperatureand relative humidity to derive at least one of the oxygen, nitrogen orwater contents of the air.
 11. The method of claim 8, wherein theoxidizing gas utilization is calculated according to the formula:Oxidizing Gas Utilization(%)=100%*((Average Cell Current (inAmps)*Number of Cells)/F)/((4*(% O2)/100%)*Cathode Flow (in mol/sec));wherein F is Faraday's constant.
 12. The method of claim 1, wherein thestep of characterizing at least one of a fuel and an oxidizing gascomprises characterizing the fuel.
 13. The method of claim 12, whereinthe fuel comprises a fuel comprising carbon and hydrogen.
 14. The methodof claim 13, wherein the fuel is selected from the group consisting ofmethane, natural gas, propane, alcohol, and syngas derived from coal ornatural gas reformation.
 15. The method of claim 12, wherein the step ofcharacterizing the fuel comprises determining a composition of the fuelbased on at least one of location or time of year.
 16. The method ofclaim 12, wherein: the fuel being provided into the fuel cell systemcomprises a mixture of two or more fuels; the step of characterizing thefuel comprises characterizing the mixture of the two or more fuels; andthe step of calculating fuel utilization comprises calculating the fuelutilization based on the step of characterizing the mixture of the twoor more fuels.
 17. The method of claim 16, wherein the two or more fuelscomprise two or more fuels with distinct carbon contents, hydrogencontents, and/or oxygen contents.
 18. The method of claim 17, wherein:the step of characterizing at least one of a fuel and an oxidizing gascomprising characterizing both the fuel and the oxidizing gas, theoxidizing gas comprises air; local atmospheric information is used tocharacterize the air; and the local atmospheric information comprisesambient temperature, ambient pressure and relative humidity.
 19. Themethod of claim 12, wherein the step of characterizing the fuelcomprises determining at least one of moles of carbon per gram ormilliliter or mole of fuel, moles of hydrogen per gram or milliliter ormole of fuel, or moles of oxygen per gram or milliliter or mole of fuel.20. The method of claim 1, wherein: the step of characterizing at leastone of a fuel and an oxidizing gas comprising characterizing both thefuel and the oxidizing gas; the step of characterizing the oxidizing gascomprises determining at least one of temperature, ambient pressure, orrelative humidity from a source of weather data; and the step ofcharacterizing the fuel comprises determining the fuel characteristicsfrom the fuel supply source or by measuring or testing the fuel.
 21. Themethod of claim 1, wherein: the fuel cell system is a solid-oxide fuelcell system; and a computer or a logic device performs the step ofcalculating.